If the magnitudes of `vec(a) xx vec(b)` equals to `vec(a). vec (b)`, then which one of the following is correct ?

Options

A. `vec(a)=vec(b)`
B. The angle between `vec(a) and vec(b)` is `45^(@)`
C. `vec(a)` is parallel to `vec(b)`
D. `vec(a)` is perpendicular to `vec(b)`

Answer

B

Explanation

Since magnitude of `vec(a)xxvec(b)=` magnitude of `vec(a).vec(b)`
`:. |vec(a)xxvec(b)|=|vec(a).vec(b)|`
`rArr |vec(a)||vec(b)|sin theta = |vec(a)||vec(b)|cos theta` (By Definition)
`rArr tan theta = 1 `
`rArr theta = (pi)/(4)`